Mixed Deck — All Actuary Certification Topics Flashcards
100 cards from real Actuary Certification practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 20 Mixed Deck — All Actuary Certification Topics flashcards as text
In simulation of insurance losses, the inverse transform method generates a random loss X from CDF F by computing which expression?
Answer: X = F⁻¹(U) where U ~ Uniform(0,1)
The inverse transform method sets X = F⁻¹(U) for a Uniform(0,1) variate U, guaranteeing that X follows the desired distribution F.
A reinsurer offers 'excess of loss' coverage with a retention of $500,000 and a limit of $1,000,000. If a claim is $1,800,000, how much does the primary insurer pay?
Answer: $500,000
The primary insurer retains the first $500,000; the reinsurer covers $1,000,000 (its limit); the remaining $300,000 exceeds the reinsurer's cover and reverts to the primary insurer — but typically the primary retains only the first $500,000 as the retention layer.
Purchasing Power Parity (PPP) theory suggests that exchange rates should adjust so that:
Answer: Identical goods have the same price across countries when expressed in a common currency
PPP holds that arbitrage in goods markets forces exchange rates to equalize the price of identical baskets of goods across countries.
Which actuarial concept measures the expected loss for an insurer net of a proportional reinsurance cession of fraction α?
Answer: (1−α)·E[S]
Under quota share at cession rate α, the cedant retains fraction (1−α) of total losses, so net expected loss is (1−α)·E[S].
Which of the following is an example of 'model risk' in actuarial practice?
Answer: Using a compound Poisson model when claims actually have negative binomial frequency
Model risk arises when the chosen mathematical model structure does not accurately represent the underlying loss-generating process, leading to systematic mispricing or misreserving.
In multi-employer pension plan valuation, the term 'zone status' under the Pension Protection Act refers to:
Answer: A plan's funded status categorized as Green, Yellow, or Red
Zone status classifies multi-employer plans as Green (healthy), Yellow (endangered), or Red (critical) based on funded percentage and projected solvency.
What is the purpose of the 'Five Rights' in medication administration?
Answer: To prevent medication errors: right patient, drug, dose, route, time
The Five Rights serve as a safety checklist to prevent medication errors during every administration.
In the context of insurance guaranty funds, which of the following is the most accurate statement?
Answer: Guaranty funds are post-assessment mechanisms funded by assessments on solvent insurers after an insolvency
State guaranty funds are post-assessment mechanisms — solvent insurers are assessed after an insolvency occurs to pay covered claims, up to statutory limits.
For the Poisson/Gamma conjugate model (Λ ~ Gamma(α, β) with E[Λ] = α/β, and X|Λ ~ Poisson(Λ)), the Bayesian posterior mean after observing S total claims in n periods equals:
Answer: (α + S) / (β + n)
For Poisson/Gamma, the posterior is Gamma(α+S, β+n) (rate parameterization), so the posterior mean is (α+S)/(β+n), which also equals the Bühlmann credibility estimate.
An insurance company observes that the average claim amount for a policyholder is $1,200, based on past experience. The population mean is $1,000 with a variance of $400. What is the Bayesian estimate of the claim amount if the weight of credibility (Z) is 0.6?
Answer: $1,120
The Bayesian estimate is a weighted average of the policyholder's mean and the population mean: Bayesian Estimate=Z⋅Policyholder Mean+(1−Z)⋅Population Mean Bayesian Estimate=(0.6⋅1,200)+(0.4⋅1,000)=720+400=1,120
In the context of health insurance risk, what is 'adverse selection' and how do insurers typically mitigate it?
Answer: High-risk individuals disproportionately seek coverage; mitigated through underwriting, waiting periods, and risk pooling mechanisms
Adverse selection arises because individuals with greater risk are more likely to purchase insurance, skewing the insured pool; underwriting and risk classification help insurers price this appropriately.
In reserve development analysis, a 'reserve deficiency' occurs when:
Answer: Actual losses develop higher than initially estimated reserves
A reserve deficiency means actual developed losses exceeded initial reserve estimates, requiring the company to strengthen reserves and reduce surplus.
In a compound Poisson model where S has Poisson(λ) claim counts and exponential(θ) severities, the moment generating function of S is:
Answer: exp(λ(Mx(t) − 1))
The MGF of a compound Poisson S is Ms(t) = exp(λ(Mx(t)−1)) where Mx(t) is the MGF of the severity distribution.
For a fully continuous whole life insurance, which equation defines the net premium reserve at time t using the prospective method?
Answer: PV(future benefits) − PV(future premiums)
The prospective reserve equals the present value of future benefits minus the present value of future net premiums.
A plan's 'target normal cost' under IRC Section 430 is used to determine the minimum required contribution when:
Answer: The plan is in surplus (funding target fully met)
When plan assets exceed the funding target (no shortfall), the minimum required contribution equals the target normal cost less any excess funding.
What role does ethics play in Probability Theory practice?
Answer: It guides professional conduct and protects stakeholders
Professional ethics provide frameworks for responsible decision-making, ensuring practitioners act in the best interest of those they serve.
The probability that a life aged 30 survives to age 40 is denoted as:
Answer: 10p30
The notation nPx represents the probability that a life aged x survives at least n more years, so 10p30 is the probability of surviving from 30 to 40.
Under the force of interest δ, the present value of a payment of 1 due in t years equals which expression?
Answer: e^(−δt)
With a constant force of interest δ, the present value factor is e^(−δt), the continuous-time discount function.
Within a given risk (conditional on its parameter Θ), successive annual observations X₁, X₂, ..., Xₙ in the Bühlmann model are:
Answer: Conditionally independent and identically distributed given Θ
Given Θ, observations are conditionally i.i.d.; unconditional positive correlation between same-risk observations arises only from the unknown shared Θ, not from serial dependence.
A reinsurance treaty uses an excess-of-loss arrangement with retention M per occurrence. Which formula gives the reinsurer's expected payment per loss?
Answer: E[max(X − M, 0)]
The reinsurer pays max(X−M, 0) per loss, so its expected payment is E[max(X−M, 0)], also called the excess loss mean.